I am a Taussky-Todd Fellow at Caltech's Division of Physics, Mathematics and Astronomy. My research uses techniques from harmonic analysis and microlocal analysis to solve problems in dispersive and nonlinear PDE, fluid dynamics, and spectral theory. I have proved sharp pointwise decay estimates for wave equations on black hole spacetimes, resolved the Onsager conjecture for SQG (with Isett), and disproved the Berger–Coburn conjecture (1991) and the Perälä–Virtanen conjecture on Toeplitz operators. Current work includes problems in fluid dynamics (Navier-Stokes, Boussinesq near Couette flow) and spectral geometry of singular domains. A unifying theme is using sharp quantitative estimates to settle conjectures at the interfaces between fields. I am also interested in AI for mathematics, including formal verification and mathematical reasoning.

I am on the job market for positions that start in 2026.